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Simplifying (4r + -2)(r + 4) = 0 Reorder the terms: (-2 + 4r)(r + 4) = 0 Reorder the terms: (-2 + 4r)(4 + r) = 0 Multiply (-2 + 4r) * (4 + r) (-2(4 + r) + 4r * (4 + r)) = 0 ((4 * -2 + r * -2) + 4r * (4 + r)) = 0 ((-8 + -2r) + 4r * (4 + r)) = 0 (-8 + -2r + (4 * 4r + r * 4r)) = 0 (-8 + -2r + (16r + 4r2)) = 0 Combine like terms: -2r + 16r = 14r (-8 + 14r + 4r2) = 0 Solving -8 + 14r + 4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 7r + 2r2) = 0 Factor a trinomial. 2((-4 + -1r)(1 + -2r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Solution
r = {-4, 0.5}
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